Transmitting Signals

ABSTRACT

A method of transmitting signals includes transmitting a signal from a plurality of antennas over a plurality of subcarriers. The signal is on-off keyed and comprises a plurality of on periods and a plurality of off periods. Each on period comprises, on each subcarrier, a frequency domain symbol associated with the subcarrier. The frequency domain symbol is phase shifted from each antenna by a respective factor of a set of factors associated with the subcarrier. The set of factors is different for at least two of the subcarriers.

RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 17/273,606, which was filed Mar. 4, 2021, which is a nationalstage application of PCT/EP2018/074158, which was filed Sep. 7, 2018,the disclosure of each of which is incorporated by reference herein inits entirety.

TECHNICAL FIELD

Examples of the present disclosure relate to transmitting signals, forexample from multiple antennas on multiple subcarriers.

BACKGROUND

Wake-up receivers (WUR), sometimes also referred to as wake-up radios,provide a means to significantly reduce the power consumption inreceivers used in wireless communication. The idea with a WUR is that itcan be based on a low-power architecture, as it only needs to be able todetect the presence of a wake-up signal. Once a wake-up signal isdetected, it may wake up another receiver used for data reception.

A commonly used modulation for a wake-up packet (WUP), i.e. a signalsent to the WUR to wake it up, is on-off keying (OOK). OOK is a binarymodulation, where a logical one is represented with sending a signal(ON) whereas a logical zero is represented by not sending a signal(OFF). A WUP may be referred to as a WUR PPDU (PLCP protocol data unit,where PLCP is Physical Layer Convergence Protocol).

FIG. 1 shows an example of a device 100 including a Wake-Up Receiver(WUR) 102. The device 100 also includes an 802.11 Primary ConnectivityRadio (PCR) 104. The WUR 102 and PCR 104 are connected to a commonantenna 106. When the WUR 102 is turned on and waiting for the wake-upsignal, the 802.11 PCR 104 can be switched off to preserve power. Oncethe wake up signal is received and detected by the WUR 102 it can wakeup the 802.11 PCR 104, which may start communicating, for example withan access point (AP) using Wi-Fi.

SUMMARY

One aspect of the present disclosure provides a method of transmittingsignals. The method comprises transmitting a first multi-carrier on-offkeyed signal comprising a plurality of on periods and a plurality of offperiods. Transmitting the first signal in each on period comprises, foreach subcarrier of a plurality of subcarriers, transmitting, from eachantenna of a plurality of antennas, a frequency domain symbol associatedwith that subcarrier phase shifted by a respective factor of a set offactors associated with that subcarrier, wherein the set of factorsassociated with that subcarrier is different from the set of factorsassociated with at least one other subcarrier of the plurality ofsubcarriers.

Another aspect of the present disclosure provides apparatus fortransmitting signals. The apparatus comprises a processor and a memory.The memory contains instructions executable by the processor such thatthe apparatus is operable to transmit a first multi-carrier on-off keyedsignal comprising a plurality of on periods and a plurality of offperiods. Transmitting the first signal in each on period comprises, foreach subcarrier of a plurality of subcarriers, transmitting, from eachantenna of a plurality of antennas, a frequency domain symbol associatedwith that subcarrier phase shifted by a respective factor of a set offactors associated with that subcarrier, wherein the set of factorsassociated with that subcarrier is different from the set of factorsassociated with at least one other subcarrier of the plurality ofsubcarriers.

A further aspect of the present disclosure provides apparatus fortransmitting signals. The apparatus is configured to transmit a firstmulti-carrier on-off keyed signal comprising a plurality of on periodsand a plurality of off periods. Transmitting the first signal in each onperiod comprises, for each subcarrier of a plurality of subcarriers,transmitting, from each antenna of a plurality of antennas, a frequencydomain symbol associated with that subcarrier phase shifted by arespective factor of a set of factors associated with that subcarrier,wherein the set of factors associated with that subcarrier is differentfrom the set of factors associated with at least one other subcarrier ofthe plurality of subcarriers.

A still further aspect of the present disclosure provides fortransmitting signals. The apparatus comprises a transmitter moduleconfigured to transmit a first multi-carrier on-off keyed signalcomprising a plurality of on periods and a plurality of off periods. Thetransmitter module is configured to transmit the first signal in each onperiod by, for each subcarrier of a plurality of subcarriers,transmitting, from each antenna of a plurality of antennas, a frequencydomain symbol associated with that subcarrier phase shifted by arespective factor of a set of factors associated with that subcarrier,wherein the set of factors associated with that subcarrier is differentfrom the set of factors associated with at least one other subcarrier ofthe plurality of subcarriers.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of examples of the present disclosure, and toshow more clearly how the examples may be carried into effect, referencewill now be made, by way of example only, to the following drawings inwhich:

FIG. 1 shows an example of a device including a Wake-Up Receiver;

FIG. 2 is a flow chart of a method of transmitting signals;

FIG. 3 is a schematic illustration of subcarriers that are transmittedfrom four antennas of an example device;

FIG. 4 shows an example of a 4×4 Discrete Fourier Transform (DFT)matrix;

FIG. 5 shows an example of factors applied to a frequency domain symboltransmitted from each subcarrier and each antenna;

FIG. 6 shows another example of factors applied to a frequency domainsymbol transmitted from each subcarrier and each antenna;

FIG. 7 shows an example of a 2×2 Discrete Fourier Transform (DFT)matrix;

FIG. 8 shows an example of factors applied to a frequency domain symboltransmitted from each subcarrier and each antenna;

FIG. 9 shows an example of general frequency domain symbols transmittedon each subcarrier and on each antenna;

FIG. 10 is a schematic of an example of apparatus for transmittingsignals; and

FIG. 11 is a schematic of an example of apparatus for transmittingsignals.

DETAILED DESCRIPTION

The following sets forth specific details, such as particularembodiments or examples for purposes of explanation and not limitation.It will be appreciated by one skilled in the art that other examples maybe employed apart from these specific details. In some instances,detailed descriptions of well-known methods, nodes, interfaces,circuits, and devices are omitted so as not obscure the description withunnecessary detail. Those skilled in the art will appreciate that thefunctions described may be implemented in one or more nodes usinghardware circuitry (e.g., analog and/or discrete logic gatesinterconnected to perform a specialized function, ASICs, PLAs, etc.)and/or using software programs and data in conjunction with one or moredigital microprocessors or general purpose computers. Nodes thatcommunicate using the air interface also have suitable radiocommunications circuitry. Moreover, where appropriate the technology canadditionally be considered to be embodied entirely within any form ofcomputer-readable memory, such as solid-state memory, magnetic disk, oroptical disk containing an appropriate set of computer instructions thatwould cause a processor to carry out the techniques described herein.

Manchester coding may be applied to data symbols of a Wake-Up Packet(WUP). That is, a data symbol comprising a logical “0” is encoded as“10” and a data symbol comprising a logical “1” as “01”. Therefore, forexample, using On-Off Keying (OOK), every data symbol comprises an “ON”part (where there is energy transmitted) and an “OFF” part, where thereis no energy transmitted. The order of the “ON” and “OFF” partsindicates whether the symbol is a logical “1” or “0”. In addition, insome examples, the signals during an “ON” period of the WUP may begenerated by means of an inverse fast Fourier transform (IFFT), as thisfunctionality already be available in some transmitters, such as forexample Wi-Fi transmitters supporting 802.11a, g, n and/or ac. Anexample IFFT has 64 points and operates at a sampling rate of 20 MHz,and just as for ordinary orthogonal frequency division multiplexing(OFDM), a cyclic prefix (CP) is added after the IFFT operation in orderto keep the OFDM symbol duration used in 802.11a/g/n/ac. An exampleapproach for generating the OOK signal is to use the 13 sub-carriers inthe center, and then populating these with signals to represent ONperiods and to not transmit anything at all during OFF periods. This maybe referred to as multicarrier OOK (MC-OOK). The same OFDM symbol may beused to generate MC-OOK. In other words, the same frequency domainsymbol is used to populate each of the non-zero subcarriers for all datasymbols. Using the same OFDM symbol to generate the “ON” part of everyManchester coded data symbol may have some advantages. For example, itallows coherent reception of the MC-OOK.

Devices such as access points may possess several transmit antennas.Hence a transmit diversity scheme may be desirable to avoidunintentional destructive interference in any particular spatialdirection. At least some embodiments of the present disclosure providemethods to generate signals such as multi-antenna MC-OOK signals, whichmay comprise wake-up packets (WUPs). In some examples, the OFDM symbolused to generate the ON part of each (e.g. Manchester coded) data symbolis antenna specific. That is, different OFDM symbols are transmittedthrough different antennas. In some examples, these antenna specificOFDM symbols may be generated by choosing the frequency domain symbolscorresponding to any given subcarrier from different entries in a column(or row) of a Discrete Fourier Transform (DFT) matrix, or for example byrotating or phase shifting a frequency domain symbol by entries in acolumn (or row) of the DFT matrix for signals transmitted on asubcarrier from multiple antennas. In some examples, when the number ofnon-zero subcarriers exceeds the number of transmit antennas, a column(or row) of the DFT matrix can be used repeatedly. In some examples,columns (or rows) are used the same number of times. In some examples,therefore, where rows (or columns) of a DFT matrix are used, orthogonalbeams may be generated, one beam per subcarrier, which in turn mayresult in an even spatial distribution of the transmitted energy of thesignals.

FIG. 2 is a flow chart of an example of a method 200 of transmittingsignals. The method may in some examples be implemented, and hence thesignals transmitted, by a device such as an access point (AP). Themethod 200 comprises, in step 202, transmitting a first multi-carrieron-off keyed (MC-OOK) signal comprising a plurality of on periods and aplurality of off periods. Transmitting the first signal in each onperiod comprises, for each subcarrier of a plurality of subcarriers, instep 204, transmitting, from each antenna of a plurality of antennas, afrequency domain symbol associated with that subcarrier phase shifted bya respective factor of a set of factors associated with that subcarrier,wherein the set of factors associated with that subcarrier is differentfrom the set of factors associated with at least one other subcarrier ofthe plurality of subcarriers.

In other words, for example, the respective set of factors applied to atleast two subcarriers is different. As a result, for example, theinterference pattern produced by transmitting signals from the antennasis different for at least two of the subcarriers.

FIG. 3 is a schematic illustration of subcarriers that are transmittedfrom four antennas of an example device. Subcarriers 302 are transmittedfrom a first antenna, subcarriers 304 are transmitted from a secondantenna, subcarriers 306 are transmitted from a third antenna andsubcarriers 308 are transmitted from a fourth antenna. Each boxrepresents one subcarrier. Where a box contains ‘0’, the subcarrier isunused (e.g. no signals are transmitted using that subcarrier from thatantenna either in an ‘ON’ or ‘OFF’ period of a MC-OOK signal). Where abox is empty, the subcarrier is used (e.g. a signal is transmitted usingthat subcarrier from that antenna in an ‘ON’ period of a MC-OOK signal).A vertical column of boxes represents one subcarrier. For example, boxes310 represent one subcarrier transmitted from each of the four antennas.A signal transmitted from the four antennas using the subcarrier 310,for example in an ‘ON’ period, may comprise for example a frequencydomain symbol shifted by a set of factors associated with thatsubcarrier. That is, a respective factor is applied to the frequencydomain symbol transmitted from each antenna for the subcarrier 310.

In some examples, the set of factors associated with each subcarriercorresponds to a row or column of a Discrete Fourier transform (DFT)matrix. In some examples, each row (or column) of the DFT matrix is usedthe minimum number of times. That is, for example, where the number ofsubcarriers is equal to the number of rows (or columns), each row (orcolumn) is used once as a set of factors for a respective subcarrier.For example, the number of subcarriers is greater than a size of the DFTmatrix, and the sets of factors associated with the subcarriers includesets corresponding to every row or column of the DFT matrix. If thenumber of subcarriers is double the number of rows (or columns), eachrow (or column) is used twice, and so on. In other examples, forexample, the number of subcarriers may be less than or equal to a sizeof the DFT matrix, and the set of factors associated with eachsubcarrier comprises a different respective row or column of the DFTmatrix.

In some examples, a matrix may be used that provides sets of factors,wherein the set of factors associated with one subcarrier is differentfrom the set of factors associated with at least one other subcarrier.In some examples, the matrix generates orthogonal beams, the DFT matrixbeing an example.

FIG. 4 shows an example of a 4×4 DFT matrix 400. FIG. 5 shows an exampleof the factors 500 applied to the frequency domain symbol transmittedfrom each subcarrier and each antenna, in an example using the DFTmatrix 400 of FIG. 4, 12 subcarriers numbered from −6 to 6 (subcarrier 0is unused), and four antennas. It can be seen that for each ofsubcarriers −6 to −3, the factors applied to the frequency domain symboltransmitted from each antenna correspond to a column (or row) of the DFTmatrix 400. Different columns of the DFT matrix are applied to thesubcarriers −6 to −3. For subcarriers −2 to 2 (not including subcarrier0), the sequence repeats, and hence different columns (or rows) of theDFT matrix 400 are applied to each of these subcarriers. Similarly, thesequence repeats for subcarriers 3 to 6. It can be seen that each of thecolumns (or rows) of the DFT matrix is used three times. In someexamples, the transmitter is used in an 802.11ba system (e.g. using a64-point DFT), in which the subcarriers are labelled −32, −31, . . . ,30, 31.

To illustrate particular subcarriers, for example subcarriers −6, −2 and3, the frequency domain symbol transmitted from each antenna is notshifted (the factor applied is 1) and the same symbol is transmitted onall of these antennas. On the other hand, for subcarriers −5, −1 and 4,the factors applied to the symbol transmitted from each antennacorrespond to the second column (or row) of the DFT matrix 400, and so adifferent symbol is transmitted from each antenna for each of thesubcarriers −5, −1 and 4.

FIG. 6 shows another example of the factors 600 applied to the frequencydomain symbol transmitted from each subcarrier and each antenna, in anexample using the DFT matrix 400 of FIG. 4, 12 subcarriers numbered from−6 to 6 (subcarrier 0 is unused), and four antennas. As in FIG. 5 , eachcolumn (or row) of the DFT matrix is used three times. However, in thiscase, the sets of factors (i.e. the columns or rows of the DFT matrix)are applied to the subcarriers in a different order.

FIG. 7 shows an example of a 2×2 Discrete Fourier Transform (DFT) matrix700. This matrix may be used in a two-antenna transmitter. In someexamples, the size of the DFT matrix matches the number of transmitantennas, though in other examples the two values may be different. Forexample, one may be an integer multiple of the other. FIG. 8 shows anexample of factors 800 applied to a frequency domain symbol transmittedfrom each subcarrier and each antenna in the two-antenna system. Eachcolumn (or row) of the DFT matrix 700 is used six times.

In some examples, the factors are all applied to the same frequencydomain symbol. However, in other examples, the factors for differentsubcarriers may be applied to different frequency domain symbols. Forexample, for a first subcarrier, the factors for that subcarrier (toproduce signals for each antenna) may be applied to a first frequencydomain symbol. For a second subcarrier, the factors for that subcarriermay be applied to a second frequency domain symbol. The first and secondfrequency domain symbols may be the same in some examples, or may bedifferent in some examples.

FIG. 9 shows an example of general frequency domain symbols transmittedon each subcarrier and on each antenna in a two-antenna system. Thecomplex phase for a frequency domain symbol associated with eachsubcarrier, on subcarriers −6 to 6 (not including subcarrier 0), isrepresented by a complex phase value a, b, c, d, e, f, g, h, i, k and lrespectively. Then, for each subcarrier, the associated frequency domainsymbol is phase shifted by the set of factors associated with thatsubcarrier to produce the set of frequency domain symbols to transmitfrom both antennas using that subcarrier. For example, for subcarrier−5, the complex phase b is shifted by the second column (or row) of the2×2 DFT matrix to produce frequency domain symbols of b and −b. Each ofthese is then transmitted on subcarrier −5 from respective antennas.

In some examples, each of the complex values a, b, c, d, e, f, g, h, i,k and l may represent a respective phase and amplitude value. In someexamples, each value of a, b, c, d, e, f, g, h, i, k and l may bedifferent, or at least some of the values may be the same. In someexamples, the same values for a, b, c, d, e, f, g, h, i, k, k and l maybe used for different ‘ON’ periods for the MC-OOK signal, whereas inother embodiments one, more than one or all of these values may varybetween ‘ON’ periods. Thus, for example, the respective frequency domainsymbol associated with one or more of the subcarriers may be the same ordifferent in different on periods.

In some examples, the plurality of subcarriers comprise orthogonalsubcarriers, e.g. the signals transmitted from one antenna on all usedsubcarriers (e.g. an OFDM symbol) are orthogonal signals.

In some examples, the first signal comprises a plurality of datasymbols, each data symbol corresponds to an on period and an off periodin a respective symbol period, and the order of the on period and theoff period in each symbol period is based on the data symbolcorresponding to the symbol period. Thus, for example, the signal maycomprise a Manchester-coded MC-OOK symbol where an OFDM symbol (e.g. amulti-carrier signal) is transmitted in each ‘ON’ period. The datasymbols in some examples may correspond to at least part of a wake uppacket (WUP), such as for example at least part of an 802.11ba WUP. Uponreceipt of the WUP, a Wake-Up Receiver (WUR) may wake up another deviceor component such as for example a Wi-Fi receiver or 802.11 PCR.

Repeated use of the same OFDM symbols to generate the ‘ON’ part of aMC-OOK signal can lead to undesirable spectral lines, because repetitionmay create strong correlations in time. This problem can be addressed insome embodiments, where a set of matrices that generate orthogonal beamsis chosen. The multi-antenna MC-OOK signal is generated as described byany of the embodiments above, but the matrix used to provide factors tobe applied to the frequency domain symbols transmitted on eachsubcarrier from each antenna may be chosen in a ransom or pseudorandomfashion, and may therefore change from one ‘ON’ period (e.g. OFDMsymbol) to the next. An example of generating a set of matricescomprises applying circular shifts to a DFT matrix. That is, forexample, all the columns of the DFT matrix are circularly shifted by thesame number of steps. In some examples, the set of matrices may consistof only two matrices, for example the DFT matrix and a second matrixobtained by circularly shifting the DFT matrix by one step (or one ormore steps for DFT matrices larger than 2×2). This randomization ofselected matrix may reduce or eliminate the above-mentioned spectrallines.

FIG. 10 is a schematic of an example of apparatus 1000 for transmittingsignals. The apparatus comprises a processor 1002 and a memory 1004. Thememory 1004 contains instructions executable by the processor 1002 suchthat the apparatus 1000 is operable to transmit a first multi-carrieron-off keyed signal comprising a plurality of on periods and a pluralityof off periods. Transmitting the first signal in each on periodcomprises, for each subcarrier of a plurality of subcarriers,transmitting, from each antenna of a plurality of antennas, a frequencydomain symbol associated with that subcarrier phase shifted by arespective factor of a set of factors associated with that subcarrier,wherein the set of factors associated with that subcarrier is differentfrom the set of factors associated with at least one other subcarrier ofthe plurality of subcarriers. In some examples, the apparatus 1000 maybe configured to carry out the method 200 of FIG. 2 . For example, thememory 1004 may contain instructions executable by the processor 1002such that the apparatus 1000 is operable to carry out the method 200 ofFIG. 2 .

FIG. 11 is a schematic of an example of apparatus 1100 for transmittingsignals. The apparatus 1100 comprises a transmitter module 1102configured to transmit a first multi-carrier on-off keyed signalcomprising a plurality of on periods and a plurality of off periods. Thetransmitter module 1102 is configured to transmit the first signal ineach on period by, for each subcarrier of a plurality of subcarriers,transmitting, from each antenna of a plurality of antennas, a frequencydomain symbol associated with that subcarrier phase shifted by arespective factor of a set of factors associated with that subcarrier,wherein the set of factors associated with that subcarrier is differentfrom the set of factors associated with at least one other subcarrier ofthe plurality of subcarriers. In some examples, the apparatus 1000 maybe configured to carry out the method 200 of FIG. 2 .

Hardware implementation may include or encompass, without limitation,digital signal processor (DSP) hardware, a reduced instruction setprocessor, hardware (e.g., digital or analogue) circuitry including butnot limited to application specific integrated circuit(s) (ASIC) and/orfield programmable gate array(s) (FPGA(s)), and (where appropriate)state machines capable of performing such functions.

It should be noted that the above-mentioned examples illustrate ratherthan limit the invention, and that those skilled in the art will be ableto design many alternative examples without departing from the scope ofthe appended statements. The word “comprising” does not exclude thepresence of elements or steps other than those listed in a claim, “a” or“an” does not exclude a plurality, and a single processor or other unitmay fulfil the functions of several units recited in the statementsbelow. Where the terms, “first”, “second” etc. are used they are to beunderstood merely as labels for the convenient identification of aparticular feature. In particular, they are not to be interpreted asdescribing the first or the second feature of a plurality of suchfeatures (i.e. the first or second of such features to occur in time orspace) unless explicitly stated otherwise. Steps in the methodsdisclosed herein may be carried out in any order unless expresslyotherwise stated. Any reference signs in the statements shall not beconstrued so as to limit their scope.

What is claimed is:
 1. A method comprising: transmitting a signal from aplurality of antennas over a plurality of subcarriers, the signal beingon-off keyed and comprising a plurality of on periods and a plurality ofoff periods, each on period comprising, on each subcarrier, a frequencydomain symbol associated with the subcarrier, the frequency domainsymbol being phase shifted from each antenna by a respective factor of aset of factors associated with the subcarrier; wherein the set offactors is different for at least two of the subcarriers.
 2. The methodof claim 1, wherein the set of factors associated with each subcarriercorresponds to a row or column of a discrete Fourier transform (DFT)matrix.
 3. The method of claim 2, wherein respective factors associatedwith each subcarrier transmitted from the same antenna correspond to acolumn or row of a DFT matrix.
 4. The method of claim 2, wherein thenumber of subcarriers is a positive integer multiple of a size of theDFT matrix.
 5. The method of claim 2, wherein the number of subcarriersis less than or equal to a size of the DFT matrix, and wherein the setof factors associated with each subcarrier comprises a differentrespective row or column of the DFT matrix.
 6. The method of claim 2,wherein the number of subcarriers is greater than a size of the DFTmatrix, and wherein the sets of factors associated with the subcarriersinclude sets corresponding to every row or column of the DFT matrix. 7.The method of claim 1, wherein at least one of the sets of factorscorresponds to no phase shift of the symbols associated with thatfactor.
 8. The method of claim 1, wherein the respective symbolassociated with each subcarrier comprises a first symbol phase shiftedby a respective amount.
 9. The method of claim 1, wherein the pluralityof subcarriers comprise orthogonal subcarriers.
 10. The method of claim1, wherein the respective symbol associated with one or more of thesubcarriers may be the same or different in different on periods. 11.The method of claim 1, wherein the signal comprises a plurality of datasymbols, each data symbol corresponding to an on period and an offperiod in a respective symbol period; and wherein the order of the onperiod and the off period in each symbol period is based on the datasymbol corresponding to the symbol period.
 12. The method of claim 11,wherein the order of the on period and the off period in each symbolperiod is selected based on Manchester coding of the corresponding datasymbol.
 13. The method of claim 11, wherein the data symbols correspondto a wake up packet (WUP).
 14. A non-transitory computer readable mediumstoring a computer program product, the computer program productcomprising program instructions which, when run on processing circuitryof an apparatus, causes the apparatus to: transmit a signal from aplurality of antennas over a plurality of subcarriers, the signal beingon-off keyed and comprising a plurality of on periods and a plurality ofoff periods, each on period comprising, on each subcarrier, a frequencydomain symbol associated with the subcarrier, the frequency domainsymbol being phase shifted from each antenna by a respective factor of aset of factors associated with the subcarrier; wherein the set offactors is different for at least two of the subcarriers.
 15. Anapparatus comprising: processing circuitry; memory containinginstructions executable by the processing circuitry whereby theapparatus is operative to: transmit a signal from a plurality ofantennas over a plurality of subcarriers, the signal being on-off keyedand comprising a plurality of on periods and a plurality of off periods,each on period comprising, on each subcarrier, a frequency domain symbolassociated with the subcarrier, the frequency domain symbol being phaseshifted from each antenna by a respective factor of a set of factorsassociated with the subcarrier; wherein the set of factors is differentfor at least two of the subcarriers.
 16. The apparatus of claim 15,wherein the set of factors associated with each subcarrier correspondsto a row or column of a discrete Fourier transform (DFT) matrix.
 17. Theapparatus of claim 16, wherein respective factors associated with eachsubcarrier transmitted from the same antenna correspond to a column orrow of a DFT matrix.
 18. The apparatus of claim 16, wherein the numberof subcarriers is a positive integer multiple of a size of the DFTmatrix.
 19. The apparatus of claim 16, wherein the number of subcarriersis less than or equal to a size of the DFT matrix, and wherein the setof factors associated with each subcarrier comprises a differentrespective row or column of the DFT matrix.
 20. The apparatus of claim16, wherein the number of subcarriers is greater than a size of the DFTmatrix, and wherein the sets of factors associated with the subcarriersinclude sets corresponding to every row or column of the DFT matrix. 21.The apparatus of claim 15, wherein at least one of the sets of factorscorresponds to no phase shift of the symbols associated with thatfactor.
 22. The apparatus of claim 15, wherein the respective symbolassociated with each subcarrier comprises a first symbol phase shiftedby a respective amount.
 23. The apparatus of claim 15, wherein theplurality of subcarriers comprise orthogonal subcarriers.
 24. Theapparatus of claim 15, wherein the respective symbol associated with oneor more of the subcarriers may be the same or different in different onperiods.
 25. The apparatus of claim 15, wherein the signal comprises aplurality of data symbols, each data symbol corresponds to an on periodand an off period in a respective symbol period; and wherein the orderof the on period and the off period in each symbol period is based onthe data symbol corresponding to the symbol period.
 26. The apparatus ofclaim 25, wherein the order of the on period and the off period in eachsymbol period is selected based on Manchester coding of thecorresponding data.